Navigation satellite systems (NSS) include both global navigation satellite systems (GNSS) and regional navigation satellite systems (RNSS), such as the Global Positioning System (GPS) (United States), GLONASS (Russia), Galileo (Europe), BeiDou (China), QZSS (Japan), and the Indian Regional Navigational Satellite System (IRNSS) (systems in use or in development). A NSS typically uses a plurality of satellites orbiting the Earth. The plurality of satellites forms a constellation of satellites. A NSS receiver detects a code modulated on an electromagnetic signal broadcast by a satellite. The code is also called a ranging code. Code detection includes comparing the bit sequence modulated on the broadcasted signal with a receiver-side version of the code to be detected. Based on the detection of the time of arrival of the code for each of a series of the satellites, the NSS receiver estimates its position. Positioning includes, but is not limited to, geolocation, i.e. the positioning on the surface of the Earth.
An overview of GPS, GLONASS and Galileo is provided for instance in sections 9, 10 and 11 of Hofmann-Wellenhof B., et al., GNSS, Global Navigation Satellite Systems, GPS, GLONASS, Galileo, & more, Springer-Verlag Wien, 2008, (hereinafter referred to as “reference [1]”).
Positioning using NSS signal codes provides a limited accuracy, notably due to the distortion the code is subject to upon transmission through the atmosphere. For instance, the GPS includes the transmission of a coarse/acquisition (C/A) code at 1575.45 MHz, the so-called L1 frequency. This code is freely available to the public, whereas the Precise (P) code is reserved for military applications. The accuracy of code-based positioning using the GPS C/A code is approximately 15 meters, when taking into account both the electronic uncertainty associated with the detection of the C/A code (electronic detection of the time of arrival of the pseudorandom code) and other errors including those caused by ionospheric and tropospheric effects, ephemeris errors, satellite clock errors and multipath propagation.
An alternative to positioning based on the detection of a code is positioning based on carrier phase measurements. In this alternative approach or additional approach (ranging codes and carrier phases can be used together for positioning), the carrier phase of the NSS signal transmitted from the NSS satellite is detected, not (or not only) the code modulated on the signal transmitted from the satellite.
The approach based on carrier phase measurements has the potential to provide much greater position precision, i.e. up to centimetre-level or even millimetre-level precision, compared to the code-based approach. The reason may be intuitively understood as follows. The code, such as the GPS C/A code on the L1 band, is much longer than one cycle of the carrier on which the code is modulated. The position resolution may therefore be viewed as greater for carrier phase detection than for code detection.
However, in the process of estimating the position based on carrier phase measurements, the carrier phases are ambiguous by an unknown number of cycles. The phase of a received signal can be determined, but the number of cycles cannot be directly determined in an unambiguous manner. This is the so-called “integer ambiguity problem”, “integer ambiguity resolution problem” or “phase ambiguity resolution problem”, which may be solved to yield the so-called fixed solution.
GNSS observation equations for code observations and for carrier phase observations are for instance provided in reference [1], section 5. An introduction to the GNSS integer ambiguity resolution problem, and its conventional solutions, is provided in reference [1], section 7.2. The skilled person will recognize that the same or similar principles apply to RNSS systems.
The main GNSS observables are therefore the carrier phase and code (pseudorange), the former being much more precise than the latter, but ambiguous. These observables basically enable a user to obtain the geometric distance from the receiver to the satellite. With known satellite position and satellite clock error, the receiver position can be estimated.
Due to different tracking and multipath mitigation technology used by different receivers or different generations of receiver board, significant receiver-dependent satellite code biases exist among different receiver models.
Yamada, H., Takasu, T., Kubo, N., Yasuda, A., Evaluation and calibration of receiver inter-channel biases for RTK-GPS/GLONASS, 23rd international technical meeting of the satellite division of the institute of navigation, Portland, Oreg., USA (2010) (hereinafter referred to as “reference [2]”), found that, for the GLONASS system, the biases may amount to several meters in the L1/L2 band.
Reussner, N., Wanninger, L. GLONASS Inter-frequency Biases and Their Effects on RTK and PPP Carrier-phase Ambiguity Resolution, Proc. of ION GNSS 2011, Portland, Oreg., USA (hereinafter referred to as “reference [3]”), found that the ionosphere-free GLONASS code biases are present also for same receiver type baselines and may amount to several meters. Furthermore, these biases cannot be modelled as a function of the GLONASS channel number k (for more details in that respect, see for example “GLONASS Interface Control Document, Navigational radiosignal In bands L1, L2”, Edition 5.1, Moscow, 2008, section 3.3.1.1: “Frequency plan”). Finally, there is evidence that, even for antipodal GLONASS satellites (same channel number k), the biases may reach the meter level. The method disclosed in reference [3] does not allow the estimation of the L1 and L2 biases separately, but only the ionosphere-free combination of such biases.
The effect of the receiver code biases per satellite is apparent when the double-difference multipath combination residuals are computed, as shown in FIG. 2.
The existence of the code biases degrades the positioning accuracy in single-receiver and differential mode. It is thus useful to remove these biases through a proper calibration process. The proper calibration of such biases improves not only the NSS positioning but also the estimates of the receiver and satellites clocks and the medium-induced delays (troposphere and ionosphere). For the end user, this may result in a better precision of the user receiver coordinates achieved in a shorter time span.
A typical calibration process is to use a zero-baseline setup (see reference [2], and Al-Shaery, A., Zhang, S., Rizos, C., An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK, GPS Solutions (2013) 17:165-173, hereinafter referred to as “reference [4]”), where at least two receivers are connected to the same physical antenna, and receivers (of the same type) are calibrated with respect to reference receivers (of the same type). With zero-baseline calibration, the code bias of each satellite can be derived from one receiver relative to a reference receiver. This approach is very accurate as the multipath, troposphere and ionosphere effects are cancelled out. The drawback is that the receivers need to be connected to the same antenna. Additional effects due to the antenna and the antenna cable are not accounted for. A zero-baseline setup is schematically illustrated in FIG. 8. The square represents the antenna, and the two rectangles represent the receiver to be calibrated and the reference receiver, respectively.
In some cases, this setup can be substituted by a short-baseline setup. The short-baseline (few meters) calibration reduces the medium-dependent errors, while the geometry is removed by the a-priori knowledge of the antenna coordinates and satellite positions. The antenna effect is accounted for in the short-baseline calibration setup, so that the approach is more suitable to calibrate smart antennas (receiver and antenna integrated in the same housing) than zero-baseline calibration. A short-baseline setup is schematically illustrated in FIG. 9.
There is a constant need for improving the implementation of positioning systems based notably on GNSS (or RNSS) carrier phase measurements, to obtain a precise estimation of the receiver position, in particular in view of the problems associated with the above-mentioned calibration approaches.